Several times here at 3fc, I've seen the folks recommend that you start by simply counting calories. As you go along, you'll figure out more about the nutritional content of foods.
For me, fat is empty calories. I can get a lot more nutrition in 100 calories of something else. Added fats are one of the easiest things to cut back on in the beginning.
You do have to read labels, like you've found with the peanutbutter.
I never worry about not getting any fat. It's very difficult to cut it out completely. Even oatmeal has a little fat content. And the odd day slipping up adds more fats than I need
My caveat is that fat has satiety value. It leaves you feeling full longer. As you go along, you'll learn how to get the same effect from protein and good whole grains.
You'll learn alot about nutrition. I sure did.